This example comes from PCA / FA (principal component analysis, factor analysis), namely from Jolliffe (see the bibliography). But it illustrates some very nice linear algebra.

More precisely, the source of this example is:

Yule, W., Berger, M., Butler, S., Newham, V. and Tizard, J. (1969). The WPPSL: An empirical evaluation with a British sample. Brit. J. Educ. Psychol., 39, 1-13.

I have not been able to find the original paper. There is a problem here, and I do not know whether the problem lies in the original paper or in Jolliffe’s version of it. If anyone out there can let me know, I’d be grateful. (I will present 3 matrices, taken from Jolliffe; my question is, does the original paper contain the same 3 matrices?)

Like the previous post on this topic, this one is self-contained. In fact, it has almost nothing to do with PCA, and everything to do with finding — or failing to find! — a transition matrix relating two matrices.

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